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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Lattice Compression of Polynomial Matrices

Li, Chao January 2007 (has links)
This thesis investigates lattice compression of polynomial matrices over finite fields. For an m x n matrix, the goal of lattice compression is to find an m x (m+k) matrix, for some relatively small k, such that the lattice span of two matrices are equivalent. For any m x n polynomial matrix with degree bound d, it can be compressed by multiplying by a random n x (m+k) matrix B with degree bound s. In this thesis, we prove that there is a positive probability that L(A)=L(AB) with k(s+1)=\Theta(\log(md)). This is shown to hold even when s=0 (i.e., where B is a matrix of constants). We also design a competitive probabilistic lattice compression algorithm of the Las Vegas type that has a positive probability of success on any input and requires O~(nm^{\theta-1}B(d)) field operations.
2

Lattice Compression of Polynomial Matrices

Li, Chao January 2007 (has links)
This thesis investigates lattice compression of polynomial matrices over finite fields. For an m x n matrix, the goal of lattice compression is to find an m x (m+k) matrix, for some relatively small k, such that the lattice span of two matrices are equivalent. For any m x n polynomial matrix with degree bound d, it can be compressed by multiplying by a random n x (m+k) matrix B with degree bound s. In this thesis, we prove that there is a positive probability that L(A)=L(AB) with k(s+1)=\Theta(\log(md)). This is shown to hold even when s=0 (i.e., where B is a matrix of constants). We also design a competitive probabilistic lattice compression algorithm of the Las Vegas type that has a positive probability of success on any input and requires O~(nm^{\theta-1}B(d)) field operations.
3

Approximate Private Quantum Channels

Dickinson, Paul January 2006 (has links)
This thesis includes a survey of the results known for private and approximate private quantum channels. We develop the best known upper bound for &epsilon;-randomizing maps, <em>n</em> + 2log(1/&epsilon;) + <em>c</em> bits required to &epsilon;-randomize an arbitrary <em>n</em>-qubit state by improving a scheme of Ambainis and Smith [5] based on small bias spaces [16, 3]. We show by a probabilistic argument that in fact the great majority of random schemes using slightly more than this many bits of key are also &epsilon;-randomizing. We provide the first known nontrivial lower bound for &epsilon;-randomizing maps, and develop several conditions on them which we hope may be useful in proving stronger lower bounds in the future.
4

Approximate Private Quantum Channels

Dickinson, Paul January 2006 (has links)
This thesis includes a survey of the results known for private and approximate private quantum channels. We develop the best known upper bound for &epsilon;-randomizing maps, <em>n</em> + 2log(1/&epsilon;) + <em>c</em> bits required to &epsilon;-randomize an arbitrary <em>n</em>-qubit state by improving a scheme of Ambainis and Smith [5] based on small bias spaces [16, 3]. We show by a probabilistic argument that in fact the great majority of random schemes using slightly more than this many bits of key are also &epsilon;-randomizing. We provide the first known nontrivial lower bound for &epsilon;-randomizing maps, and develop several conditions on them which we hope may be useful in proving stronger lower bounds in the future.

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